Critical points of higher order for the normal map of immersions in R^d

We study the critical points of the normal map v : NM -> Rk+n, where M is an immersed k-dimensional submanifold of Rk+n, NM is the normal bundle of M and v(m, u) = m + u if u is an element of NmM. Usually, the image of these critical points is called the focal set. However, in that set there is a subset where the focusing is highest, as happens in the case of curves in R-3 with the curve of the centers of spheres with contact of third order with the curve. We give a definition of r-critical points of a smooth map between manifolds, and apply it to study the 2 and 3-critical points of the normal map in general and the 2-critical points for the case k = n = 2 in detail. In the later case we analyze the relation with the strong principal directions of Montaldi (1986) [2]. (C) 2011 Elsevier B.V. All rights reserved.Work partially supported by CAPES (BEX 4533/06-2).Monera, M.; Montesinos-Amilibia, A.; Moraes, S.; Sanabria Codesal, E. (2012). Critical points of higher order for the normal map of immersions in R^d. Topology and its Applications. 159:537-544. https://doi.org/10.1016/j.topol.2011.09.029S53754415

Phenotype Harmonization in the GLIDE2 Oral Health Genomics Consortium

Genetic risk factors play important roles in the etiology of oral, dental, and craniofacial diseases. Identifying the relevant risk loci and understanding their molecular biology could highlight new prevention and management avenues. Our current understanding of oral health genomics suggests that dental caries and periodontitis are polygenic diseases, and very large sample sizes and informative phenotypic measures are required to discover signals and adequately map associations across the human genome. In this article, we introduce the second wave of the Gene-Lifestyle Interactions and Dental Endpoints consortium (GLIDE2) and discuss relevant data analytics challenges, opportunities, and applications. In this phase, the consortium comprises a diverse, multiethnic sample of over 700,000 participants from 21 studies contributing clinical data on dental caries experience and periodontitis. We outline the methodological challenges of combining data from heterogeneous populations, as well as the data reduction problem in resolving detailed clinical examination records into tractable phenotypes, and describe a strategy that addresses this. Specifically, we propose a 3-tiered phenotyping approach aimed at leveraging both the large sample size in the consortium and the detailed clinical information available in some studies, wherein binary, severity-encompassing, and ?precision,? data-driven clinical traits are employed. As an illustration of the use of data-driven traits across multiple cohorts, we present an application of dental caries experience data harmonization in 8 participating studies (N = 55,143) using previously developed permanent dentition tooth surface?level dental caries pattern traits. We demonstrate that these clinical patterns are transferable across multiple cohorts, have similar relative contributions within each study, and thus are prime targets for genetic interrogation in the expanded and diverse multiethnic sample of GLIDE2. We anticipate that results from GLIDE2 will decisively advance the knowledge base of mechanisms at play in oral, dental, and craniofacial health and disease and further catalyze international collaboration and data and resource sharing in genomics research

Recurrent Coding Sequence Variation Explains only A Small Fraction of the Genetic Architecture of Colorectal Cancer

Whilst common genetic variation in many non-coding genomic regulatory regions are known to impart risk of colorectal cancer (CRC), much of the heritability of CRC remains unexplained. To examine the role of recurrent coding sequence variation in CRC aetiology, we genotyped 12,638 CRCs cases and 29,045 controls from six European populations. Single-variant analysis identified a coding variant (rs3184504) in SH2B3 (12q24) associated with CRC risk (OR = 1.08, P = 3.9 × 10-7), and novel damaging coding variants in 3 genes previously tagged by GWAS efforts; rs16888728 (8q24) in UTP23 (OR = 1.15, P = 1.4 × 10-7); rs6580742 and rs12303082 (12q13) in FAM186A (OR = 1.11, P = 1.2 × 10-

Meta-analysis of Genome-Wide Association Studies for Extraversion: Findings from the Genetics of Personality Consortium

Extraversion is a relatively stable and heritable personality trait associated with numerous psychosocial, lifestyle and health outcomes. Despite its substantial heritability, no genetic variants have been detected in previous genome-wide association (GWA) studies, which may be due to relatively small sample sizes of those studies. Here, we report on a large meta-analysis of GWA studies for extraversion in 63,030 subjects in 29 cohorts. Extraversion item data from multiple personality inventories were harmonized across inventories and cohorts. No genome-wide significant associations were found at the single nucleotide polymorphism (SNP) level but there was one significant hit at the gene level for a long non-coding RNA site (LOC101928162). Genome-wide complex trait analysis in two large cohorts showed that the additive variance explained by common SNPs was not significantly different from zero, but polygenic risk scores, weighted using linkage information, significantly predicted extraversion scores in an independent cohort. These results show that extraversion is a highly polygenic personality trait, with an architecture possibly different from other complex human traits, including other personality traits. Future studies are required to further determine which genetic variants, by what modes of gene action, constitute the heritable nature of extraversion

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Introduction: More than 70 common alleles are known to be involved in breast cancer (BC) susceptibility, and several exhibit significant heterogeneity in their associations with different BC subtypes. Although there are differences in the association patterns between BRCA1 and BRCA2 mutation carriers and the general population for several loci, no study has comprehensively evaluated the associations of all known BC susceptibility alleles with risk of BC subtypes in BRCA1 and BRCA2 carriers. Methods: We used data from 15,252 BRCA1 and 8,211 BRCA2 carriers to analyze the associations between approximately 200,000 genetic variants on the iCOGS array and risk of BC subtypes defined by estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2) and triple-negative- (TN) status; morphologic subtypes; histological grade; and nodal involvement. Results: The estimated BC hazard ratios (HRs) for the 74 known BC alleles in BRCA1 carriers exhibited moderate correlations with the corresponding odds ratios from the general population. However, their associations with ER-positive BC in BRCA1 carriers were more consistent with the ER-positive as

Identification of common genetic risk variants for autism spectrum disorder

Autism spectrum disorder (ASD) is a highly heritable and heterogeneous group of neurodevelopmental phenotypes diagnosed in more than 1% of children. Common genetic variants contribute substantially to ASD susceptibility, but to date no individual variants have been robustly associated with ASD. With a marked sample-size increase from a unique Danish population resource, we report a genome-wide association meta-analysis of 18,381 individuals with ASD and 27,969 controls that identified five genome-wide-significant loci. Leveraging GWAS results from three phenotypes with significantly overlapping genetic architectures (schizophrenia, major depression, and educational attainment), we identified seven additional loci shared with other traits at equally strict significance levels. Dissecting the polygenic architecture, we found both quantitative and qualitative polygenic heterogeneity across ASD subtypes. These results highlight biological insights, particularly relating to neuronal function and corticogenesis, and establish that GWAS performed at scale will be much more productive in the near term in ASD.Peer reviewe

Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus

A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P=9.2 × 10-20), ER-negative BC (P=1.1 × 10-13), BRCA1-associated BC (P=7.7 × 10-16) and triple negative BC (P-diff=2 × 10-5). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P=2 × 10-3) and ABHD8 (P<2 × 10-3). Chromosome conformation capture identifies interactions between four candidate SNPs and ABHD8, and luciferase assays indicate six risk alleles increased transactivation of the ADHD8 promoter. Targeted deletion of a region containing risk SNP rs56069439 in a putative enhancer induces ANKLE1 downregulation; and mRNA stability assays indicate functional effects for an ANKLE1 3′-UTR SNP. Altogether, these data suggest that multiple SNPs at 19p13 regulate ABHD8 and perhaps ANKLE1 expression, and indicate common mechanisms underlying breast and ovarian cancer risk

Genome-Wide Association Study in BRCA1 Mutation Carriers Identifies Novel Loci Associated with Breast and Ovarian Cancer Risk

BRCA1-associated breast and ovarian cancer risks can be modified by common genetic variants. To identify further cancer risk-modifying loci, we performed a multi-stage GWAS of 11,705 BRCA1 carriers (of whom 5,920 were diagnosed with breast and 1,839 were diagnosed with ovarian cancer), with a further replication in an additional sample of 2,646 BRCA1 carriers. We identified a novel breast cancer risk modifier locus at 1q32 for BRCA1 carriers (rs2290854, P = 2.7×10-8, HR = 1.14, 95% CI: 1.09-1.20). In addition, we identified two novel ovarian cancer risk modifier loci: 17q21.31 (rs17631303, P = 1.4×10-8, HR = 1.27, 95% CI: 1.17-1.38) and 4q32.3 (rs4691139, P = 3.4×10-8, HR = 1.20, 95% CI: 1.17-1.38). The 4q32.3 locus was not associated with ovarian cancer risk in the general population or BRCA2 carriers, suggesting a BRCA1-specific associat

Multi-ancestry GWAS of the electrocardiographic PR interval identifies 202 loci underlying cardiac conduction

The electrocardiographic PR interval reflects atrioventricular conduction, and is associated with conduction abnormalities, pacemaker implantation, atrial fibrillation (AF), and cardiovascular mortality. Here we report a multi-ancestry (N = 293,051) genome-wide association meta-analysis for the PR interval, discovering 202 loci of which 141 have not previously been reported. Variants at identified loci increase the percentage of heritability explained, from 33.5% to 62.6%. We observe enrichment for cardiac muscle developmental/contractile and cytoskeletal genes, highlighting key regulation processes for atrioventricular conduction. Additionally, 8 loci not previously reported harbor genes underlying inherited arrhythmic syndromes and/or cardiomyopathies suggesting a role for these genes in cardiovascular pathology in the general population. We show that polygenic predisposition to PR interval duration is an endophenotype for cardiovascular disease, including distal conduction disease, AF, and atrioventricular pre-excitation. These findings advance our understanding of the polygenic basis of cardiac conduction, and the genetic relationship between PR interval duration and cardiovascular disease

Multi-ancestry genome-wide association analyses improve resolution of genes and pathways influencing lung function and chronic obstructive pulmonary disease risk.

Lung-function impairment underlies chronic obstructive pulmonary disease (COPD) and predicts mortality. In the largest multi-ancestry genome-wide association meta-analysis of lung function to date, comprising 580,869 participants, we identified 1,020 independent association signals implicating 559 genes supported by ≥2 criteria from a systematic variant-to-gene mapping framework. These genes were enriched in 29 pathways. Individual variants showed heterogeneity across ancestries, age and smoking groups, and collectively as a genetic risk score showed strong association with COPD across ancestry groups. We undertook phenome-wide association studies for selected associated variants as well as trait and pathway-specific genetic risk scores to infer possible consequences of intervening in pathways underlying lung function. We highlight new putative causal variants, genes, proteins and pathways, including those targeted by existing drugs. These findings bring us closer to understanding the mechanisms underlying lung function and COPD, and should inform functional genomics experiments and potentially future COPD therapies